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Édouard Zeckendorf (1901–1983) was a Belgian doctor and army officer. He took an interest in mathematics, particularly Fibonacci numbers. These are the numbers defined by the recurrence *Fn*+2 = *Fn*+1 + *Fn for n ≥ 0, with F*1 = F0 = 1.
A theorem bears his name—relatively rare for an amateur. It states that every integer is a sum of distinct Fibonacci numbers. Moreover, this representation is unique if no two of the Fibonacci numbers are consecutive.
Thus, 8 = F4 + F2 + F0 = 5 + 2 + 1. If consecutive Fibonacci numbers are allowed, we also have 8 = F4 + F3 = 5 + 3 and 8 = F4 + F2 + F1 = 5 + 2 + 1. Zeckendorf said he discovered this result in 1939. Other mathematicians popularized it in the 1950s—duly crediting Zeckendorf with the discovery—before he published it himself in 1972.
In the grip of pentagons... ---------------------------------